1. Field of the Invention
The present invention generally relates to the framework for machine cognition, and more particularly to a method and system for signal processing of combinatorial logic in a network.
2. Discussion of the Background
Originally the Kanban cell (KC) was the production part of a linear pull system used to minimize the size, change, and turnover of parts inventory for the Just in Time (JIT) manufacturing of automobiles.
FIG. 1 shows the KC in the Petri net, a bipartite directed graph, and with or without a failure or idle subnet as an abstraction of the generalized stochastic Petri net (GSPN) of flexible manufacturing systems (FMS), which are push production systems (for example, using pallets to load incomplete parts and to unload completed parts by continuous transportation as by conveyer or automatic guided vehicle (AGV)).
In FIG. 1, system 10 is a Petri net of a Kanban cell (KC) disclosed in Colin James III, Recent Advances in Logic Tables for Reusable Database Engines, Proceedings of the American Society of Mechanical Engineers International, Petroleum Division, Energy Sources Technology Conference & Exhibition, Houston, Tex., ETCE99-6628, 1999 (“James 1999”), herein incorporated by reference in its entirety for all purposes. Step 104 is a transition. Step 101 is the input and output place. Steps 105 and 106 are feedback paths of the feedback loops of the paths 103 to 104 and 102 to 104. In this context, feedback paths serve as decision branches in the logic of the KC, and are commonly referred to in their totality as feedback loops. (Steps marked as m1, m2, m6, and t2 are true to the original labels and equivalent to the respective Steps 101, 102, 103, and 104.)
FIG. 2 shows similarity between the structure of the KC and the design of a universal accounting arithmetic system in N-dimensions, disclosed in James 1999 and Colin James III, A Reusable Database Engine for Accounting Arithmetic, Proceedings of the Third Biennial World Conference on Integrated Design & Process Technology, Vol. 2, p. 25-30, Berlin, Germany, 1998 (“James 1998”), herein incorporated by reference in its entirety for all purposes. Steps 201, 202, and 203 are descriptive of the respective symbols of Steps 101, 102, and 103 in FIG. 1. Steps 204, 205, and 206 are descriptive of the respective symbol of Step 104 in FIG. 1. Step 207 is keyed to the respective Step 107 in FIG. 1. Steps in FIG. 2 describe how a KC system performs the identical functionality of a disparate system, heretofore not related solely to the field of manufacturing, and hence indicate that the KC is a universal mechanism for abstract processing of any kind.
In FIG. 2, system 20 is an accounting arithmetic system disclosed in James 1998. Step 201 inputs a transaction type and the amount on which to operate. Step 202 uses a look up table (LUT) to translate the transaction type into an output index code. Step 203 uses another LUT to obtain the series of sequential logic switches by which to operate on the amount from Step 201. The input index of Step 203 is the output index of Step 202. Step 204 is the output of the account indexes and respective operators. The input index of Step 204 is the output from Step 203. Step 205 operates the series of sequential accounts by which the respective operators process the amount from Step 201. The accounts contain only a single balance value which is updated and overwritten. Step 206 is the update step by which an unbounded transaction log records the transaction type and amount from Step 201 and also a unique time stamp that verifies when Steps 201 through Step 205 are completed. Step 207 is a feedback loop from Steps 206 to Step 201 to restart the process for further inputs.
FIG. 3 shows a synchronous, self-timing neural network as a series of feedback loops.
In FIG. 3, system 30 is a neural network. System 30 consists of data places, through which data flows as data places 301, 311, and 321, and of timing places as timing places 302, 312, and 322, which stimulate the data places as 301, 311, and 321. The direction the data flows is bidirectional as in paths 305 and 306. The direction of timing paths is bidirectional as in paths 303 and 304. The timing places 302, 312, and 322 effectively open and close the data places 301, 311, and 321 to control when waiting data is allowed to flow. The timing places 302, 312, and 322 may be either physical clock cycles or logical looping structures, the duration for which constitutes a delay in system 30.
In biology, a neuron is a cell nucleus and body with multiple dendrites as input paths, and a single axon as output path. The entry pathway of the dendrite to the neuron cell is a synapse and receptor where in the neurotransmitter fluid such as serotonin, ion transfers occur with calcium (Ca+), potassium (K+), and sodium (Na+).
Neural components can be represented as vector spaces such as an adaptive linear neuron or adaptive linear element (Adaline) composed of weight and bias vectors with a summation function (OR circuit), and also a multi-layered Adaline (Madaline) where two such units emulate a logical XOR function (exclusive OR circuit). Such components are examples of probabilistic methodology applied as an apparatus to map and mimic the biological neuron.
A “perceptron” can be represented as a binary classifier using a dot product to convert a real-valued vector to a single binary value which serves as a probabilistic methodology and apparatus to map and mimic the biological neuron.
A “spike neuron” or “spiking neuron” can be represented as a conductive network based on temporal or time bias and differential equations or calculus which serves as a probabilistic methodology and apparatus to map and mimic the biological neuron.
One deficiency with the neural network in the related art is that as it is based on a vector space, a solution is ultimately not bivalent, is probabilistic, and hence is undecidable. (That bivalency is not a vector space is disclosed in Colin James III, Proof of Four Valued Bit Code (4 vbc) as a Group, Ring, and Module, World Congress and School on Universal Logic III, Estoril, Portugal, 2010 (“James 2010”), herein incorporated by reference in its entirety for all purposes.)
Another deficiency is that an exclusive OR (XOR) function is sometimes mistankenly developed in a neural network to mimic a neuron. The logical XOR connective is orthogonal or effectively perpendicular as a mathematical operator. However, biological bodies are not rectilinear, but rather based on a phi or Phi ratio of (1±(5^0.5))/2, and meaning that there are no right angles (90-degree arcs) in biology per se. While the logical XOR connective may be constructed from the NOR or NAND logical connectives, there is no evidence that the XOR function is built into the neuron, or necessarily should be.
Yet another deficiency with the related art is that the perceptron and spike neuron can accept any input without discrimination.